CN108730267B - Open pump control asymmetric cylinder system position sensitivity analysis method - Google Patents
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Abstract
A position sensitivity analysis method for an open pump-controlled asymmetric cylinder system comprises the following steps: dividing the open pump-controlled asymmetric cylinder system into a plurality of independent modules; step 2: assuming that the pressure loss in the pipeline and the valve cavity is zero and the liquid is incompressible, the mathematical model of each module can be obtained by analyzing the structural principle of each module on the basis, and different elements are selected, wherein the mathematical models of the modules are different; and step 3: analyzing the system, and obtaining a mathematical model of the pump control system by combining mathematical models of the modules through a flow continuity equation and a stress balance equation; and 4, step 4: and (4) carrying out sensitivity analysis on the system, and judging the influence degree of each parameter change on the displacement output dynamic process through two sensitivity measurement indexes. The invention can qualitatively analyze the steady-state influence of each parameter on the displacement output, can quantitatively analyze the influence degree of each parameter on the displacement output dynamic process, and provides a theoretical basis for the performance optimization of the pump-controlled asymmetric cylinder system.
Description
Technical Field
The invention relates to a position sensitivity analysis method for an open pump-controlled asymmetric cylinder system.
Background
With the increasing concern about energy shortage, the research on energy conservation of hydraulic transmission systems is receiving extensive attention. The application of the pump control technology is one of effective methods for reducing the energy consumption of the hydraulic system, and in order to reduce the energy consumption of the hydraulic system, the most direct method is to adopt the pump control technology. However, the pump-controlled asymmetric cylinder system still has the problems of slow response speed, serious nonlinearity, low control precision and the like. In order to solve the above problems, scholars at home and abroad propose various control methods, such as an adaptive control method, a nonlinear control method, a hybrid control method, a simple adaptive control method based on a pump-controlled asymmetric cylinder system, and the like.
Although the dynamic and static characteristics of the position control process of the pump-controlled asymmetric cylinder system can be improved to a certain extent by adopting an advanced control theory, the influence degree of each key parameter of the pump-controlled system on the output characteristics of the system is explored by a position sensitivity analysis method to obtain a decisive influence parameter, reference is provided for the design of a controller, and the dynamic and static characteristics of the position control of the pump-controlled asymmetric cylinder system are further improved.
Disclosure of Invention
The invention aims to provide a position sensitivity analysis method based on an open type pump-controlled asymmetric cylinder system, which can be used for exploring the influence degree of each key parameter of a pump-controlled system on the output characteristic of the system and providing a theoretical basis for the performance optimization of the pump-controlled asymmetric cylinder system.
A position sensitivity analysis method based on an open pump control asymmetric cylinder system comprises the following steps:
step 1: dividing the open pump-controlled asymmetric cylinder system into a plurality of independent modules, including: the hydraulic control system comprises a hydraulic power module, a hydraulic control module and an execution module.
The hydraulic power module is used for providing system power, namely hydraulic energy;
the hydraulic control module is used for controlling the pressure, flow and flow direction of working media in the system;
the executing module, namely the controlled object, has the function of performing corresponding linear reciprocating motion according to the requirement of the control module.
Step 2: on the assumption that the pressure loss in the pipeline and the valve cavity is zero and the liquid is incompressible, on the basis, the mathematical model of each module can be obtained by analyzing the structural principle of each module, and different elements are selected, wherein the mathematical model of each module is different.
And step 3: and analyzing the system, and obtaining the mathematical model of the pump control system by combining the mathematical models of the modules through a flow continuity equation and a stress balance equation.
And 4, step 4: and (4) carrying out sensitivity analysis on the system, and judging the influence degree of each parameter change on the displacement output dynamic process through two sensitivity measurement indexes.
Compared with the prior art, the invention has the following advantages: the method not only can qualitatively analyze the steady-state influence of each parameter on displacement output, but also can quantitatively analyze the influence degree of each parameter on the displacement output dynamic process, thereby providing a theoretical basis for the performance optimization of the pump-controlled asymmetric cylinder system.
Drawings
FIG. 1 is a schematic diagram of an open pump hydraulic system of the present invention;
FIG. 2 is a graph of sensitivity index for each parameter of the present invention;
FIG. 3 is a position control simulation model of the open pump-controlled asymmetric cylinder system of the present invention.
Detailed Description
Example implementations will now be described more fully with reference to the accompanying drawings. The exemplary embodiments, however, may be embodied in many different forms and should not be construed as limited to the examples set forth herein. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, apparatus, steps, and so forth.
A position sensitivity analysis method based on an open pump control asymmetric cylinder system comprises the following steps:
step 1: dividing the open pump-controlled asymmetric cylinder system into a plurality of independent modules, including: the hydraulic control system comprises a hydraulic power module, a hydraulic control module and an execution module;
the hydraulic power module selects a proportional variable radial plunger pump (RKP variable pump) of MOOG company as a power source;
a hydraulic control module; compared with the traditional valve control system, the hydraulic valve is used for carrying out relevant control, and the pump control system selects a hydraulic pump as a control module, namely an RKP pump is a power module and is also a control module;
and the execution module selects the asymmetric hydraulic cylinder.
Step 2: on the basis of the assumption that the pressure loss in the pipeline and the valve cavity is zero and the liquid is incompressible, the mathematical model of each module can be obtained by analyzing the structural principle of each module.
The mathematical model of the RKP variable displacement pump as the main element is as follows:
in the formula, KpqIs the flow gain of the variable displacement pump, KsFor servo valve gain, TsAs servo valve time constant, KaFor amplifier gain, UinFor servo valve command voltage signals, UfFeeding back a voltage signal, K, to the servovalvexStroke Loop position gain, XsEccentricity of stroke ring, P being pressure at variable pump port, CtpTo the external leakage coefficient of variable displacement pumps, AsIs the area of the servo cylinder.
And step 3: and analyzing the system, and obtaining the mathematical model of the pump control system by combining the mathematical models of the modules through a flow continuity equation and a stress balance equation.
The equation of state of a general system is expressed as (the following formula is a general formula, and unconditional conditions hold)
Where x is a dimensional state vector, u is an r-dimensional input independent of α, α is a P-dimensional parameter, and t is time.
The highest order of the open pump control asymmetric cylinder system is 8 orders, 8 state variables, 1 input and 21 parameter items are selected, and each vector of the formula (1) is expressed as
x＝(x1,x2,x3,x4,x5,x6,x7,x8)T
u＝(u1)T
α＝(α1，α2，α3，α4，α5，α6，α7，α8，α9，α10，α11，α12，α13，α14，α15，α16，α17，α18，α19，α20,α21)T
(2)；
Wherein the state variables in the state vector x are
x1＝Qs1，x2＝Qs2，x3＝Xs1，x4＝Xs2，
x5＝P1，x6＝P2，x7＝y，x8＝y&
The input in the input vector u is
u1＝Yin
The parameter in the parameter α vector is
α1＝Ks1,α2＝Ks2,α3＝Ts1,α4＝Ts2,
α5＝As1,α6＝As2,α7＝Kp,α8＝Kqp1,
α9＝Kqp2,α10＝l0,α11＝Ctp1,α12＝Ctp2,
α13＝A1,α14＝A2,α15＝Cec1,α15＝Cec2,
α16＝Cec2,α17＝Be,α18＝mt,α19＝Bp,
α20＝FL,α21＝K
In the formula, FLFor external load force, KPFor system proportional gain, mtTo carry an equivalent mass, betaeIs the bulk modulus of elasticity, A1Is the effective area of the master cylinder, A2Effective area of the return cylinder, K load spring rate, l0Is the initial position of the movable beam, BpIs a viscous damping coefficient, Cec1Is the leakage coefficient outside the master cylinder, Cec2To return coefficient of out-of-cylinder leakage, Ctp1Is the leakage coefficient, C, of the servo variable pump 2tp2For the outside leakage coefficient, K, of the servo variable pump 1s1For servo variable pump 2 pilot stage servo valve gain, Ks2For servo variable pump 1 pilot stage servo valve gain, Ts1Is the time constant of a pilot stage servo valve of a servo variable pump 2s2Is the time constant of a pilot stage servo valve of a servo variable pump 1, As1For the area of the cylinder of the pilot stage servo valve of the servo variable pump 2, As2For the area of the cylinder of the pilot-stage servo valve of the servo variable pump 1, Ka1Amplification gain, K, for the pilot-stage servo valve of the servo variable pump 2a2The gain is amplified for the pilot stage servo valve of the servo variable pump 1.
That is, formula (1) can be arranged as
And 4, step 4: and (4) carrying out sensitivity analysis on the system, and judging the influence degree of each parameter change on the displacement output dynamic process through two sensitivity measurement indexes.
Selecting system parameters for sensitivity analysis includes: according to the structural parameters of each element obtained in the system state equation; and physical parameters such as leakage coefficient, liquid effective volume elastic modulus and the like are used as sensitivity analysis parameter vectors.
The solution of equation (1) can be expressed as:
wherein n represents the nth state vector,
is a function symbol, alpha is a p-dimensional parameter, and t is time.
The sensitivity function of the state vector x to the parameter α is defined as:
wherein i represents the ith parameter and n represents the nth state vector;
in the case where u and α are independent of each other, equation (3) simultaneously derives the partial derivative of the parameter vector α on both sides of the equation:
wherein,
in order to be a factor term of the sensitivity equation,
is a free term of the sensitivity equation.
According to the sensitivity function expression, a sensitivity function time-course curve corresponding to each parameter can be obtained through Matlab calculation and is used as a basis for judging the influence degree of each parameter on the steady-state characteristic of the system.
The two sensitivity measurement indexes selected by the invention are respectively as follows: the peak sensitivity and the mean sensitivity are calculated according to the following formula:
peak sensitivity calculation formula:
in the formula, the delta x represents the state vector change lambada in represents the sensitivity function delta ai represents the ith vector change, and xsj represents the steady-state value of the hydraulic cylinder relative to the displacement step quantity of the hydraulic cylinder;
mean sensitivity calculation formula:
according to the two sensitivity measurement indexes, the obtained bar chart can be used as a basis for quantitatively analyzing the influence degree of each parameter on the system output dynamic characteristic.
In order to prove the beneficial effect of the technical scheme of the invention, a group of principles based on a 0.6MN pump-controlled hydraulic machine and a hydraulic system are provided below, as shown in figure 1, and each parameter is a sensitivity index obtained according to the formula.
The obtained sensitivity bar chart is shown in figure 2 according to the position sensitivity analysis method of the open type pump control asymmetric cylinder system, and the figure shows that the gain alpha of the pilot stage servo valve of the servo variable pump 21Pilot stage servo valve time constant alpha of servo variable pump 2 and servo variable pump 13、α4The sensitivity indexes 1 are all larger than 0.75%, the sensitivity indexes 2 are all larger than 2.5mm, and the sensitivity indexes 2 are all larger than 7mm, so that the three parameters have larger influence on x7 in the dynamic process. Gain of pilot stage servo valve of servo variable pump 1 and area alpha of pilot stage oil cylinder of servo variable pump 22、α5Proportional gain alpha7Servo variable pump 2 flow gain alpha8The sensitivity indexes 1 are all around 0.25%, the trends of the sensitivity indexes 2 are the same, the influence degree is the next order, and the two sensitivity indexes of the rest parameters are very small and have small influence degree.
Selecting the proportional gain alpha of the system7And the initial position alpha of the movable beam10And (3) carrying out experimental verification to measure the output displacement of the master cylinder, subtracting the output displacement before parameter change, calculating the maximum value of deviation and the sum of absolute values of all the deviations, and in order to ensure the accuracy of the test result, adopting a multi-sample averaging method to obtain two sensitivity index test values and a simulation comparison bar chart of the 2 parameters in a sorting mode, wherein the two sensitivity index test values and the simulation comparison bar chart are shown in fig. 3.
It can be seen from fig. 3 that the difference between the sensitivity index experimental value and the theoretical value of the two parameters is not large, and the sensitivity index theoretical value is larger than the experimental value under the loading condition, which means that the loading force has certain fluctuation. But the proportion of the sensitivity index of each parameter is in accordance with the theory, which fully proves the accuracy of theoretical analysis.
Claims (4)
1. A position sensitivity analysis method for an open pump-controlled asymmetric cylinder system is characterized by comprising the following steps: the method comprises the following steps: step 1: the open pump control asymmetric cylinder system is divided into a plurality of independent modules, wherein each independent module comprises a hydraulic power module, a hydraulic control module and an execution module, and the hydraulic power module is used for providing system power, namely hydraulic energy; the hydraulic control module is used for controlling the pressure, flow and flow direction of working media in the system; the execution module is a controlled object, and the action of the execution module carries out corresponding linear reciprocating motion according to the requirement of the control module; step 2: assuming that the pressure loss in the pipeline and the valve cavity is zero and the liquid is incompressible, the mathematical model of each module can be obtained by analyzing the structural principle of each module on the basis, and different elements are selected, wherein the mathematical models of the modules are different; and step 3: analyzing the system, and obtaining a mathematical model of the pump control system by combining mathematical models of the modules through a flow continuity equation and a stress balance equation, wherein a state equation of a general system is expressed as
Formula (1) is a general formula, and the unconditional condition is satisfied, wherein x is a state vector, u is r-dimensional input irrelevant to alpha, alpha is a P-dimensional parameter, and t is time; and 4, step 4: and (3) carrying out sensitivity analysis on the system, wherein the two selected sensitivity measurement indexes are respectively as follows: and judging the influence degree of each parameter change on the displacement output dynamic process through two sensitivity measurement indexes, wherein the larger the two sensitivity values are, the higher the influence degree is, and the smaller the value is, the smaller the influence degree is.
2. The method for analyzing the position sensitivity of the open pump-controlled asymmetric cylinder system according to claim 1, characterized in that: in step 3, the highest order of the open pump-controlled asymmetric cylinder system is 8 orders, and 8 state variables, 1 input and 21 parameter items are selected;
each vector of equation (1) is represented as
x＝(x1,x2,x3,x4,x5,x6,x7,x8)T
u＝(u1)T
α＝(α1，α2，α3，α4，α5，α6，α7，α8，α9，α10，α11，α12，α13，α14，α15，α16，α17，α18，α19，α20,α21)T
(2)；
Wherein the state variables in the state vector x are
X1＝Qs1，X2＝Qs2，X3＝Xs1，X4＝Xs2，
X5＝P1，X6＝P2，X7＝y，X8＝y&
The input in the input vector u is
u1＝Yin
The parameter in the parameter α vector is
α1＝Ks1,α2＝Ks2,α3＝Ts1,α4＝Ts2,
α5＝As1,α6＝As2,α7＝Kp,α8＝Kqp1,
α9＝Kqp2,α10＝l0,α11＝Ctp1,α12＝Ctp2,
α13＝A1,α14＝A2,α15＝Cec1,α15＝Cec2,
α16＝Cec2,α17＝Be,α18＝mt,α19＝Bp,
α20＝FL,α21＝K
In the formula, FLFor external load force, KPFor system proportional gain, mtTo carry an equivalent mass, betaeIs the bulk modulus of elasticity, A1Is the effective area of the master cylinder, A2Effective area of the return cylinder, K load spring rate, l0Is the initial position of the movable beam, BpIs a viscous damping coefficient, Cec1Is the leakage coefficient outside the master cylinder, Cec2To return coefficient of out-of-cylinder leakage, Ctp1Is the leakage coefficient, C, of the servo variable pump 2tp2For the outside leakage coefficient, K, of the servo variable pump 1s1For servo variable pump 2 pilot stage servo valve gain, Ks2For servo variable pump 1 pilot stage servo valve gain, Ts1Is the time constant of a pilot stage servo valve of a servo variable pump 2s2Is the time constant of a pilot stage servo valve of a servo variable pump 1, As1For the area of the cylinder of the pilot stage servo valve of the servo variable pump 2, As2For the area of the cylinder of the pilot-stage servo valve of the servo variable pump 1, Ka1Amplification gain, K, for the pilot-stage servo valve of the servo variable pump 2a2The gain is amplified by a pilot stage servo valve of a servo variable pump 1, namely formula (2) is finished,
3. the method for analyzing the position sensitivity of the open pump-controlled asymmetric cylinder system according to claim 1, characterized in that: in step 4, selecting system parameters for sensitivity analysis includes: according to the structural parameters of each element obtained in the system state equation; physical parameters such as leakage coefficient, liquid effective volume elastic modulus and the like are used as sensitivity analysis parameter vectors,
the solution of equation (1) can be expressed as:
wherein n represents the nth state vector,
for the function sign, α is a p-dimensional parameter, and t is the sensitivity function of the time state vector x to the parameter α defined as:
wherein i represents the ith parameter and n represents the nth state vector;
in the case where u and α are independent of each other, equation (3) simultaneously derives the partial derivative of the parameter vector α on both sides of the equation:
wherein,
in order to be a factor term of the sensitivity equation,
and (3) obtaining a sensitivity function time-course curve corresponding to each parameter through Matlab calculation according to a sensitivity function expression as a free item of a sensitivity equation and using the sensitivity function time-course curve as a basis for judging the influence degree of each parameter on the steady-state characteristic of the system.
4. The open pump-controlled asymmetric cylinder system position sensitivity analysis method according to claim 1 or 3, characterized in that: in step 4, the two selected sensitivity measurement indexes are respectively: the peak sensitivity and the mean sensitivity are calculated according to the following formula:
peak sensitivity calculation formula:
in the formula, the delta x represents the state vector change lambada in represents the sensitivity function delta ai represents the ith vector change, and xsj represents the steady-state value of the hydraulic cylinder relative to the displacement step quantity of the hydraulic cylinder;
mean sensitivity calculation formula:
according to the two sensitivity measurement indexes, the obtained bar chart can be used as a basis for quantitatively analyzing the influence degree of each parameter on the system output dynamic characteristic.
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